Dwight Diller sings this song on his New Plowed Ground CD, but it's hard to hear the words. Two of the verses are:

Muskrat, muskrat, what makes your head so red?
(can't hear the rest)

Muskrat, muskrat, where you been so long?
Way down yonder in the farmer's field
Eatin' up the farmer's corn, eatin' up the farmer's corn

Muskrat, muskrat, what makes your head so brown?
Lived in a hole (???)
Way down under the ground, way down under the ground.

Muskrat, muskrat, what makes your tail so bare?
Way down yonder where I live,
It don't need no hair, it don't need no hair.